Session: 7.7.1 - Numerical Methods for Multiphase Flows I

Paper Number: 158484

158484 - A Coupled Finite Volume / Material Point Method for Compressible Gas-Liquid Two-Phase Flows for Application to Atomization 

Abstract: 

This focus of this study is to develop a robust coupled Lagrangian (liquid) / Eulerian (gas) modeling paradigm for describing shear induced atomization.  The eventual application of interest is atomization of melting paraffin wax in a slab burner experiments, for understanding the dynamics of hybrid rocket motors.  From a modeling standpoint, the fundamental challenge describing shear atomization is the accurately tracking the formation of ligaments, their instability growth and finally pinch-off forming droplets.   While volume of fluid (VOF) methods has been used for this purpose historically, they often suffer from numerical diffusion resulting in loss of fluid.  The appeal of a mixed liquid phase Lagrangian and gas phase Eulerian formulation is two-fold.  The first is the elimination of convective diffusion errors. The second is the ability to map resolved liquid scales to unresolved scales for describing subgrid droplets via lumped descriptions.    In this effort, a mixed numerical methodology is presented using Material Point Methods (MPM) for the liquid phases and coupled with Eulerian gas phase field CFD using a new stratified flow approximation.   The MPM formulation is based on a generalized interpolation material point (GIMP) using convected particle domain interpolation (CPDI) techniques.  In this approach, the material points are described using first-order Lagrange elements. MPM element level subgrid models are introduced to account for changes in drag forces acting on the liquid as it transitions from CFD resolved to unresolved scales.  The CFD approach is based on a finite volume formulation for compressible flows employing AUSMUP+ flux vector splitting and high-order Runge-Kutta time integration.  To couple the phases, a volume fraction based stratified description is introduced that enforces zero gas pressure gradient at the gas-liquid interface.  Several 1D benchmark problems are first presented to explore error convergence rates and the stability of the overall algorithm.  These benchmarks are useful for demonstrating the stratified flow coupling algorithm satisfies the pressure non-disturbance condition for a perfect shift condition.     Simulations of millimeter sized colliding 2D liquid rings are then presented for assessing the limits of the interface reconstruction and sensitivity to gas coupling.  Results from the colliding rings show the overall coupling methodology is robust and is useful for exploring atomization processes.

Presenting Author: Paul DesJardin SUNY Buffalo

Presenting Author Biography: